A piecewise linearization framework for retail shelf space management models

Managing shelf space is critical for retailers to attract customers and optimize profits. This article develops a shelf-space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. A piecewise linearization technique is used to approximate the complicated nonlinear space-allocation model. The approximation reformulates the non-convex optimization problem into a linear mixed integer programming (MIP) problem. The MIP solution not only generates near-optimal solutions for large scale optimization problems, but also provides an error bound to evaluate the solution quality. Consequently, the proposed approach can solve single category-shelf space management problems with as many products as are typically encountered in practice and with more complicated cost and profit structures than currently possible by existing methods. Numerical experiments show the competitive accuracy of the proposed method compared with the mixed integer nonlinear programming shelf-space model. Several extensions of the main model are discussed to illustrate the flexibility of the proposed methodology.     

Confidence estimation for tolerance intervals

The post-data performances of normal tolerance intervals are studied. Under a robust Bayesian predictive scheme, we establish the ordering and bounds of the confidence estimators. It is found that the nominal confidence coefficient tends to be extreme yet coincides with the limiting Bayes estimators in some scenarios. A remark on the choice of beta priors is also given.     

Off-axis performance analysis of wavefront coded imaging system

Point spread functions at different field angles and phase deviations of the cubic mask are used for image restoration to analyze the off-axis performance of a wavefront coded imaging system.     

Improvement of productivity of yeast cell with a novel airlift loop reactor

Applied Biochemistry and Biotechnology - Two different strains of baker’s yeast are cultivated using a fed-batch process with a novel airlift loop reactor. The reactor can be operated not...     

A dual perturbation view of linear programming

Solving standard-form linear prograrns via perturbation of the primal objective function has received much attention recently. In this paper, we investigate a new perturbation scheme which obtains a dual optimal solution by perturbing the dual feasible domain under different norms. A dual-to-primal conversion formula is also provided. We show that this new perturbation scheme actually generalizes the primal entropic perturbation approach to linear programming.Partially sponsored by the North Carolina Supercomputing Center 1994 Cray Research Grant and the National Textile Center Research Grant.     

Nonrenormalizability of Einstein-Yang-Mills interactions at the one-loop level

The interactions between the quantized Einstein and quantized Yang-Mills fields are one-loop nonrenormalizable.     

Quantitative nanoorganized structural evolution for a high efficiency bulk heterojunction polymer solar cell

We have developed an improved small-angle X-ray scattering (SAXS) model and analysis methodology to quantitatively evaluate the nanostructures of a blend system. This method has been applied to resolve the various structures of self-organized poly(3-hexylthiophene)/C61-butyric acid methyl ester (P3HT/PCBM) thin active layer in a solar cell from the studies of both grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence X-ray diffraction (GIXRD). Tuning the various length scales of PCBM-related structures by a different annealing process can provide a flexible approach and better understanding to enhance the power conversion of the P3HT/PCBM solar cell. The quantitative structural characterization by this method includes (1) the mean size, volume fraction, and size distribution of aggregated PCBM clusters, (2) the specific interface area between PCBM and P3HT, (3) the local cluster agglomeration, and (4) the correlation length of the PCBM molecular network within the P3HT phase. The above terms are correlated well with the device performance. The various structural evolutions and transformations (growth and dissolution) between PCBM and P3HT with the variation of annealing history are demonstrated here. This work established a useful SAXS approach to present insight into the modeling of the morphology of P3HT/PCBM film. In situ GISAXS measurements were also conducted to provide informative details of thermal behavior and temporal evolution of PCBM-related structures during phase separation. The results of this investigation significantly extend the current knowledge of the relationship of bulk heterojunction morphology to device performance.     

Effect of hydroxypropyl-β-cyclodextrin complexation on the aqueous solubility, structure, thermal stability, antioxidant activity, and tyrosinase inhibition of paeonol

The objective of this paper is to study the effect of hydroxypropyl-β-cyclodextrin (HP-β-CD) complexation on the aqueous solubility, structure, thermal stability, antioxidant activity, and tyrosinase inhibition of paeonol (PAE). The inclusion complex (PAE-HP-β-CD complex) of HP-β-CD and PAE was prepared by a freeze-drying method. Phase solubility tests showed that the stability constant of the inclusion complex was about 33.8?M^?1 at 25?°C. The experimental results of proton nuclear magnetic resonance (H-NMR) spectroscopy, differential scanning calorimetry (DSC) and X-ray diffraction (XRD) suggested that PAE was included by HP-β-CD to form the PAE-HP-β-CD complex. Furthermore, the thermogravimetric analysis (TGA) results showed that the thermal stability of PAE was improved when it was complexed with HP-β-CD. Comparing the antioxidant activity of PAE with that of the PAE-HP-β-CD complex at the same concentration revealed that the complex of PAE with HP-β-CD was better able to eliminate radical. Furthermore, the experimental results revealed that the formation of a complex with HP-β-CD increased the water solubility of PAE, improving its apparent inhibitive activity of tyrosinase.     

Donnan potential of dilute colloidal dispersions: Monte Carlo simulations

Donnan equilibrium between a salt-free colloidal dispersion and an electrolyte solution has been investigated by Monte Carlo simulations. The Donnan potential is directly calculated by considering two compartments separated by a semipermeable membrane. In order to understand the role played by colloid–ion interactions, the influences of colloidal characteristics, including particle size R, intrinsic particle charge Z, counterion valency z_c, and concentration c_p, on Donnan potential Ψ_D and effective charge Z_eff are examined. Our simulations show that the electroneutrality condition is not followed in both compartments and the Donnan potential arises due to the net charge density. The Donnan potential grows by increasing c_p and Z_eff and by decreasing dielectric constant ε_r, i.e., Ψ_DZ_effc_p/ε_r approximately. Note that the effective charge varies with R,Z,c_p,ε_r and z_c as well. When the salt concentration is increased, the net charge density is lowered and thus the Donnan potential decays accordingly. The validity of the classical theory based on the Nernst equation and the electroneutrality assumption is also examined. In general, the simulation results at high-salt condition can be well represented by such mean-field theory.